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Brian May #1
Brian May is most famous as the lead guitarist for the British rock band Queen. Before he became a rock star, he was a Ph.D. student in astrophysics; he published two papers before putting his academic career on hold. In the 2000s, May went back to Imperial College London and finally completed his degree.
May can claim an Erdős number of 5 through his popular science books written with Chris Lintott and Sir Patrick Moore. A stronger (if longer) path can be traced through a Nature paper he published in the '70s about the zodiacal light. It is no surprise that he has a Sabbath number of 1: he has a guitar solo on the Sabbath album Headless Cross. May's Bacon number comes from a voice role in The Adventures of Pinocchio.
(suggested by Chris Lintott)
There is a longer (length 7) collaboration path between May and Erdős using only published journal articles: